Jess Chen
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Think of the linear PLL model as a linearization about an operating point, something like the linearization SPICE does about a DC operating point. A better analogy is the linearization of switch mode power supplies. You can think of the linear PLL model as a state space averaged model. The linear model is good for small signal analysis. As for acquisition transients, AFTER you account for frequency slewing, if you are using a phase frequency detector, the near-linear response of the PLL dominates the remaining transient.
-Jess
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